# Stored data for newform 690.2.a.g, downloaded from the LMFDB on 19 April 2024.
{"label": "690.2.a.g", "space_label": "690.2.a", "level": 690, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021597797778098, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 133030106766864329, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[7, [2, 1]], [11, [2, 1]], [17, [4, 1]]], "qexp_display": "q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2760, "fricke_eigenval": 1, "atkin_lehner_string": "-++-", "analytic_conductor": 5.509677739468347, "hecke_ring_index": 1, "level_radical": 690, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [690, 1, [461, 277, 511], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5, 23], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.036", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.078", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.172", "prec": 17}], "related_objects": ["EllipticCurve/Q/690/g"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [5, 1], [23, -1]], "trace_display": [1, -1, -1, -2], "traces": [0, 1, 1, -1, 1, -1, -1, -2, 1, 1, -1, -2, -1, -6, -2, 1, 1, -4, 1, 0, -1, 2, -2, 1, -1, 1, -6, -1, -2, 2, 1, 0, 1, 2, -4, 2, 1, -8, 0, 6, -1, -6, 2, -4, -2, -1, 1, 0, -1, -3, 1, 4, -6, 6, -1, 2, -2, 0, 2, 0, 1, -8, 0, -2, 1, 6, 2, -4, -4, -1, 2, 16, 1, 6, -8, -1, 0, 4, 6, 14, -1, 1, -6, 14, 2, 4, -4, -2, -2, -8, -1, 12, 1, 0, 0, 0, -1, -6, -3, -2, 1, 6, 4, -2, -6, -2, 6, -18, -1, -4, 2, 8, -2, 12, 0, -1, 2, -6, 0, 8, 1, -7, -8, 6, 0, -1, -2, 0, 1, 4, 6, 12, 2, 0, -4, 1, -4, -8, -1, -4, 2, 0, 16, 12, 1, -2, 6, 3, -8, 10, -1, 12, 0, -4, 4, 0, 6, -16, 14, -6, -1, -2, 1, -4, -6, -2, 14, 0, 2, 23, 4, 0, -4, 18, -2, -2, -2, 0, -8, -20, -1, -12, 12, 8, 1, 8, 0, 8, 0, 2, 0, 0, -1, -2, -6, -6, -3, 6, -2, -2, 1, 4, 6, -4, 4, 6, -2, 1, -6, 0, -2, -20, 6, -16, -18, 4, -1, 0, -4, -6, 2, 24, 8, -16, -2, 1, 12, -18, 0, -20, -1, -4, 2, -26, -6, 0, 0, -14, 8, 16, 1, -14, -7, -1, -8, 3, 6, 0, 0, -14, -1, 6, -2, -2, 0, -4, 1, 14, 4, 16, 6, 2, 12, 4, 2, -6, 0, 8, -4, -18, 1, 20, -4, -12, -8, -2, -1, -10, -4, 0, 2, 8, 0, -16, 16, 0, 12, 12, 1, -1, -2, 6, 6, -10, 3, 0, -8, 2, 10, -6, -1, 8, 12, -6, 0, 8, -4, 28, 4, 2, 0, -32, 6, -34, -16, 2, 14, -22, -6, -4, -1, 18, -2, 0, 1, -6, -4, 4, -6, 0, -2, 20, 14, -8, 0, 4, 2, -34, 23, -12, 4, 0, 0, 20, -4, 1, 18, -8, -2, -6, -2, 6, -2, 26, 0, -16, -8, -8, -20, 24, -1, -19, -12, 7, 12, -6, 8, 10, 1, -6, 8, -12, 0, 32, 8, 1, 0, -12, 2, 16, 0, 0, 0, -12, -1, -4, -2, -4, -6, 10, -6, -4, -3, -12, 6, -14, -2, -22, -2, 0, 1, -24, 4, 0, 6, -1, -4, 16, 4, 38, 6, 8, -2, 0, 1, -14, -6, 4, 0, -14, -2, 0, -20, 0, 6, -4, -16, 16, -18, -12, 4, -36, -1, 30, 0, 2, -4, 0, -6, 32, 2, -3, 24, 4, 8, 8, -16, -10, -2, -22, 1, 12, 12, -12, -18, -12, 0, 18, -20, 4, -1, -10, -4, -36, 2, 0, -26, -30, -6, 8, 0, 16, 0, 8, -14, 0, 8, 6, 16, 8, 1, 48, -14, 2, -7, 6, -1, 12, -8, 4, 3, -12, 6, -8, 0, 2, 0, -32, -14, -28, -1, 0, 6, 4, -2, -6, -2, -23, 0, -14, -4, -12, 1, 0, 14, 2, 4, 0, 16, -18, 6, -4, 2, 4, 12, 2, 4, 0, 2, 1, -6, 0, 0, 36, 8, 18, -4, 20, -18, 6, 1, 26, 20, 12, -4, 4, -12, 12, -8, -8, -2, 0, -1, -28, -10, -8, -4, -22, 0, 24, 2, -8, 8, -10, 0, -12, -16, -2, 16, 24, 0, 12, 12, 0, 12, 1, 1, 2, -1, 2, -2, -28, 6, -12, 6, 6, -10, 8, 3, 0, 0, -6, -8, 30, 2, -8, 10, 2, -6, -24, -1, -22, 8, -4, 12, 7, -6, 40, 0, 4, 8, 0, -4, -4, 28, -6, 4, 28, 2, 0, 0, -1, -32, 16, 6, 1, -34, 0, -16, 32, 2, -22, 14, 20, -22, 0, -6, 18, -4, 16, -1, 16, 18, -28, -2, -4, 0, -24, 1, 0, -6, 0, -4, 22, 4, -12, -6, 6, 0, 6, -2, 0, 20, -24, 14, 0, -8, 2, 0, 16, 4, 16, 2, 42, -34, -1, 23, 2, -12, 12, 4, 18, 0, 48, 0, 8, 20, 20, -4, -36, 1, 28, 18, 4, -8, 4, -2, 24, -6, 26, -2, 30, 6, 0, -2, 0, 26, -12, 0, 16, -16, 14, -8, 0, -8, -12, -20, -16, 24, 24, -1, 4, -19, 14, -12, 2, 7, 38, 12, 1, -6, 16, 8, 36, 10, -3, 1, 8, -6, 12, 8, 0, -12, 4, 0, -10, 32, 14, 8, 36, 1, -50, 0, -6, -12, -12, 2, 40, 16, 2, 0, -10, 0, 8, 0, 4, -12, 0, -1, 6, -4, -14, -2, -18, -4, 0, -6, -16, 10, 0, -6, -32, -4, -2, -3, 16, -12, -4, 6, -4, -14, -24, -2, 48, -22, 6, -2, -46, 0, 0, 1, -8, -24, -12, 4, 2, 0, 18, 6, -18, -1, -44, -4, -20, 16, 4, 4, 0, 38, 12, 6, -10, 8, -4, -2, 2, 0, -22, 1, -38, -14, 10, -6, 12, 4, 0, 0, 0, -14, -20, -2, -25, 0, -8, -20, -23, 0, 14, 6, 16, -4, -8, -16, 26, 16, 0, -18, 30, -12, -12, 4, -12, -36, 24, -1, -18, 30, 1, 0, -28, 2, 24, -4, -6, 0, 2, -6, -2, 32, 10, 2, -56, -3, -36, 24, 0, 4, 48, 8, 0, 8, -2, -16, 0, -10, 20, -2, 6, -22, 0, 1, -24, 12, -8, 12, 12, -12, -24, -18, 6, -12, 36, 0, -28, 18, -8, -20, -24, 4, -2, -1, -28, -10, -96, -4, -8, -36, -2, 2, 18, 0, 0, -26, 32, -30, -8, -6, 42, 8, 34, 0, -22, 16, -6, 0, -2, 8, 8, -14, -36, 0, 22, 8, 44, 6, 0, 16, 4, 8, 16, 1, -31, 48, -18, -14, 2, 2, 52, -7, 0, 6, -46, -1, 8, 12, 6, -8, 24, 4, 16, 3, -4, -12, -12, 6, -6, -8, 0, 0, -4, 2, -32, 0, -20, -32, 2, -14, -2, -28, 8, -1], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "690.2.a.g", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [1], [-1], [1], [-1], [-1], [-2], [1], [1], [-1], [-2], [-1], [-6], [-2], [1], [1], [-4], [1], [0], [-1], [2], [-2], [1], [-1], [1], [-6], [-1], [-2], [2], [1], [0], [1], [2], [-4], [2], [1], [-8], [0], [6], [-1], [-6], [2], [-4], [-2], [-1], [1], [0], [-1], [-3], [1], [4], [-6], [6], [-1], [2], [-2], [0], [2], [0], [1], [-8], [0], [-2], [1], [6], [2], [-4], [-4], [-1], [2], [16], [1], [6], [-8], [-1], [0], [4], [6], [14], [-1], [1], [-6], [14], [2], [4], [-4], [-2], [-2], [-8], [-1], [12], [1], [0], [0], [0], [-1], [-6], [-3], [-2], [1]]}